結果
| 問題 | No.1780 [Cherry Anniversary] 真冬に咲く26の櫻の木 |
| コンテスト | |
| ユーザー |
👑  Kazun
|
| 提出日時 | 2026-02-26 00:24:46 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 251 ms / 2,000 ms |
| コード長 | 21,882 bytes |
| 記録 | |
| コンパイル時間 | 5,079 ms |
| コンパイル使用メモリ | 409,620 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2026-02-26 00:24:58 |
| 合計ジャッジ時間 | 10,566 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge6 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 42 |
ソースコード
#line 1 "1780.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1780"
#line 2 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 2 "/home/user/competitive_programming/library_for_cpp/template/utility.hpp"
using ll = long long;
// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
return (a < b ? a = b, 1: 0);
}
// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
return (a > b ? a = b, 1: 0);
}
// a の最大値を取得する.
template<typename T>
inline T max(const vector<T> &a){
if (a.empty()) throw invalid_argument("vector is empty.");
return *max_element(a.begin(), a.end());
}
// vector<T> a の最小値を取得する.
template<typename T>
inline T min(const vector<T> &a){
if (a.empty()) throw invalid_argument("vector is empty.");
return *min_element(a.begin(), a.end());
}
// vector<T> a の最大値のインデックスを取得する.
template<typename T>
inline size_t argmax(const vector<T> &a){
if (a.empty()) throw std::invalid_argument("vector is empty.");
return distance(a.begin(), max_element(a.begin(), a.end()));
}
// vector<T> a の最小値のインデックスを取得する.
template<typename T>
inline size_t argmin(const vector<T> &a){
if (a.empty()) throw invalid_argument("vector is empty.");
return distance(a.begin(), min_element(a.begin(), a.end()));
}
#line 61 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
// math
#line 2 "/home/user/competitive_programming/library_for_cpp/template/math.hpp"
// 演算子
template<typename T>
T add(const T &x, const T &y) { return x + y; }
template<typename T>
T sub(const T &x, const T &y) { return x - y; }
template<typename T>
T mul(const T &x, const T &y) { return x * y; }
template<typename T>
T neg(const T &x) { return -x; }
template<typename T>
T bitwise_and(const T &x, const T &y) { return x & y; }
template<typename T>
T bitwise_or(const T &x, const T &y) { return x | y; }
template<typename T>
T bitwise_xor(const T &x, const T &y) { return x ^ y; }
// 除算に関する関数
// floor(x / y) を求める.
template<typename T, typename U>
T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); }
// ceil(x / y) を求める.
template<typename T, typename U>
T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;}
// x を y で割った余りを求める.
template<typename T, typename U>
T safe_mod(T x, U y){
T q = div_floor(x, y);
return x - q * y ;
}
// x を y で割った商と余りを求める.
template<typename T, typename U>
pair<T, T> divmod(T x, U y){
T q = div_floor(x, y);
return {q, x - q * y};
}
// 四捨五入を求める.
template<typename T, typename U>
T round(T x, U y){
T q, r;
tie (q, r) = divmod(x, y);
return (r >= div_ceil(y, 2)) ? q + 1 : q;
}
// 指数に関する関数
// x の y 乗を求める.
ll intpow(ll x, ll y){
ll a = 1;
while (y){
if (y & 1) { a *= x; }
x *= x;
y >>= 1;
}
return a;
}
// x の y 乗を z で割った余りを求める.
ll modpow(ll x, ll y, ll z){
ll a = 1;
while (y){
if (y & 1) { (a *= x) %= z; }
(x *= x) %= z;
y >>= 1;
}
return a;
}
// x の y 乗を z で割った余りを求める.
template<typename T, typename U>
T modpow(T x, U y, T z) {
T a = 1;
while (y) {
if (y & 1) { (a *= x) %= z; }
(x *= x) %= z;
y >>= 1;
}
return a;
}
// vector の要素の総和を求める.
ll sum(vector<ll> &X){
ll y = 0;
for (auto &&x: X) { y+=x; }
return y;
}
// vector の要素の総和を求める.
template<typename T>
T sum(vector<T> &X){
T y = T(0);
for (auto &&x: X) { y += x; }
return y;
}
template<typename T>
T sum(const vector<T> &X) {
T y = T(0);
for (auto &&x: X) { y += x; }
return y;
}
// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
template<integral T>
tuple<T, T, T> Extended_Euclid(T a, T b) {
T s = 1, t = 0, u = 0, v = 1;
while (b) {
T q;
tie(q, a, b) = make_tuple(div_floor(a, b), b, safe_mod(a, b));
tie(s, t) = make_pair(t, s - q * t);
tie(u, v) = make_pair(v, u - q * v);
}
return make_tuple(s, u, a);
}
// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) {
if (N <= 0) { return 0; }
ll x = sqrt(N);
while ((x + 1) * (x + 1) <= N) { x++; }
while (x * x > N) { x--; }
return x;
}
// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }
// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
ll x = isqrt(N);
return x * x == N ? x : x + 1;
}
#line 64 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
// inout
#line 1 "/home/user/competitive_programming/library_for_cpp/template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }
void print(){ cout << "\n"; }
template<class T, class... Ts>
void print(const T& a, const Ts&... b){
cout << a;
(cout << ... << (cout << " ", b));
cout << "\n";
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
is >> P.first >> P.second;
return is;
}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
os << P.first << " " << P.second;
return os;
}
template<typename T>
vector<T> vector_input(int N, int index){
vector<T> X(N+index);
for (int i=index; i<index+N; i++) cin >> X[i];
return X;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &X){
for (auto &x: X) { is >> x; }
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
int s = (int)X.size();
for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
int i = 0;
for (T a: S) {os << (i ? " ": "") << a; i++;}
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
template<typename T>
std::vector<T> input_vector(size_t n, size_t offset = 0) {
std::vector<T> res;
// 最初に必要な全容量を確保（再確保を防ぐ）
res.reserve(n + offset);
// offset 分をデフォルト値で埋める（特別 indexed 用）
res.assign(offset, T());
for (size_t i = 0; i < n; ++i) {
T el;
if (!(std::cin >> el)) break;
res.push_back(std::move(el));
}
return res;
}
#line 67 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
// macro
#line 2 "/home/user/competitive_programming/library_for_cpp/template/macro.hpp"
// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)
// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name
// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 70 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
// bitop
#line 2 "/home/user/competitive_programming/library_for_cpp/template/bitop.hpp"
// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
if (x == 0) { return 0; }
return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}
// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }
// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }
// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }
// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }
// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
vector<int> bits(k);
rep(i, k) {
bits[i] = x & 1;
x >>= 1;
}
return bits;
}
// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 73 "/home/user/competitive_programming/library_for_cpp/template/template.hpp"
// exception
#line 2 "/home/user/competitive_programming/library_for_cpp/template/exception.hpp"
class NotExist: public exception {
private:
string message;
public:
NotExist() : message("求めようとしていたものは存在しません.") {}
const char* what() const noexcept override {
return message.c_str();
}
};
#line 2 "/home/user/competitive_programming/library_for_cpp/Algebra/Extended_Algebra.hpp"
#line 4 "/home/user/competitive_programming/library_for_cpp/Algebra/Extended_Algebra.hpp"
class IndeterminateOperationError : public std::runtime_error {
public:
IndeterminateOperationError(const std::string& msg): std::runtime_error(msg) {}
};
template<typename R>
struct Extended_Algebra {
R val;
signed char inf_flag; // 0: finite, 1: +inf, -1: -inf
constexpr Extended_Algebra(R val, signed char inf_flag): val(val), inf_flag(inf_flag) {}
public:
constexpr Extended_Algebra(): val(R()), inf_flag(0) {}
constexpr Extended_Algebra(R val): val(val), inf_flag(0) {}
constexpr Extended_Algebra operator-() const { return Extended_Algebra(-val, -inf_flag); }
static constexpr Extended_Algebra inf = Extended_Algebra(R(), 1);
constexpr bool is_finite() const { return inf_flag == 0; }
constexpr bool is_infinite() const { return !is_finite(); }
constexpr bool is_positive(const bool zero = false) const {
if(is_infinite()) { return inf_flag > 0; }
return zero ? val >= R() : val > R();
}
constexpr bool is_negative(const bool zero = false) const {
if(is_infinite()) { return inf_flag < 0; }
return zero ? val <= R() : val < R();
}
constexpr bool is_positive_infinite() const { return inf_flag == 1; }
constexpr bool is_negative_infinite() const { return inf_flag == -1; }
constexpr inline bool is_zero() const { return inf_flag == 0 && val == R(); }
constexpr Extended_Algebra& operator+=(const Extended_Algebra &rhs) {
if (is_positive_infinite() && rhs.is_negative_infinite()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf + (-inf))");
}
if (is_negative_infinite() && rhs.is_positive_infinite()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form ((-inf) + inf)");
}
if (is_finite() && rhs.is_finite()) { val += rhs.val; }
else if (is_positive_infinite() || rhs.is_positive_infinite()) { inf_flag = 1; }
else if (is_negative_infinite() || rhs.is_negative_infinite()) { inf_flag = -1; }
return *this;
}
friend constexpr Extended_Algebra operator+(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) += rhs; }
constexpr Extended_Algebra& operator-=(const Extended_Algebra &rhs) {
if (this->is_positive_infinite() && rhs.is_positive_infinite()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf - inf)");
}
if (this->is_negative_infinite() && rhs.is_negative_infinite()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form ((-inf) - (-inf))");
}
if (is_finite() && rhs.is_finite()) { val -= rhs.val; }
else if (is_positive_infinite() || rhs.is_negative_infinite()) { inf_flag = 1; }
else if (is_negative_infinite() || rhs.is_positive_infinite()) { inf_flag = -1; }
return *this;
}
friend constexpr Extended_Algebra operator-(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) -= rhs; }
constexpr Extended_Algebra& operator*=(const Extended_Algebra &rhs) {
if (is_zero() || rhs.is_zero()) {
val = R();
inf_flag = 0;
return *this;
}
if (is_finite() && rhs.is_finite()) { val *= rhs.val; return *this; }
if (is_positive() == rhs.is_positive()) { inf_flag = 1; }
else { inf_flag = -1; }
return *this;
}
friend constexpr Extended_Algebra operator*(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) *= rhs; }
constexpr Extended_Algebra& operator/=(const Extended_Algebra &rhs) {
// 0-1. 未定義形: (± inf) / (± inf)
if (this->is_infinite() && rhs.is_infinite()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf / inf)");
}
// 0-2. 未定義形: 0 / 0
if (this->is_zero() && rhs.is_zero()) {
throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (0 / 0)");
}
// 1. ゼロ除算: finite (non-zero) / 0 -> ±inf
if (rhs.is_zero()) {
// 分母が 0 であるが, 0-2 を通り抜けているので, 分子が 0 にはなり得ない.
inf_flag = is_positive() ? 1 : -1;
val = R();
return *this;
}
// 2. どちらも有限 (分母 != 0)
if (is_finite() && rhs.is_finite()) {
// ゼロ除算は上記 1 で処理済み
val /= rhs.val;
return *this;
}
// 3. 無限大を含む確定的な計算
// inf / finite (non-zero) または finite (zero) / inf
val = R(); // 結果は inf / 0
if (this->is_infinite() && rhs.is_finite()) {
// inf / finite -> 符号は乗算と同じ
inf_flag = (is_positive() == rhs.is_positive()) ? 1 : -1;
} else { // finite / inf -> 0 (既に is_zero()で処理されているべきだが安全のため)
inf_flag = 0;
}
return *this;
}
// 非複合演算子
friend constexpr Extended_Algebra operator/(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) /= rhs; }
// 比較
friend constexpr bool operator==(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {
if (lhs.inf_flag != rhs.inf_flag) { return false; }
if (lhs.is_finite()) { return lhs.val == rhs.val; }
return true;
}
friend constexpr bool operator<(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {
if (lhs.inf_flag != rhs.inf_flag) { return lhs.inf_flag < rhs.inf_flag; }
if (lhs.is_finite()) { return lhs.val < rhs.val; }
return false;
}
friend constexpr bool operator!=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return !(lhs == rhs);}
friend constexpr bool operator> (const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return rhs < lhs;}
friend constexpr bool operator<=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return (lhs < rhs) || (lhs == rhs);}
friend constexpr bool operator>=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return (lhs > rhs) || (lhs == rhs);}
// 出力
friend ostream &operator<<(ostream &os, const Extended_Algebra &x) {
if (x.is_positive_infinite()) { return os << "inf"; }
if (x.is_negative_infinite()) { return os << "-inf"; }
return os << x.val;
}
};
#line 2 "/home/user/competitive_programming/library_for_cpp/Algebra/Semiring_Matrix.hpp"
#line 4 "/home/user/competitive_programming/library_for_cpp/Algebra/Semiring_Matrix.hpp"
template<class Semiring, auto ADD, auto zero, auto MUL, auto one>
class Semiring_Matrix {
public:
int row, col;
Semiring_Matrix() : row(0), col(0) {}
Semiring_Matrix(int n): Semiring_Matrix(n, n) {}
Semiring_Matrix(int n, int m) : row(n), col(m), mat(n, vector<Semiring>(m, zero)) {}
Semiring_Matrix(const vector<vector<Semiring>>& mat) : row(mat.size()), col(mat.size() ? mat[0].size() : 0), mat(mat) {}
inline const vector<Semiring>& operator[](int i) const { return mat[i]; }
inline vector<Semiring>& operator[](int i) { return mat[i]; }
inline const Semiring& operator[](int i, int j) const { return mat[i][j]; }
inline Semiring& operator[](int i, int j) { return mat[i][j]; }
static Semiring_Matrix identity(int n) {
Semiring_Matrix res(n, n);
for (int i = 0; i < n; ++i) res[i][i] = one;
return res;
}
Semiring_Matrix& operator+=(const Semiring_Matrix& b) {
assert(row == b.row && col == b.col);
for (int i = 0; i < row; ++i) {
for (int j = 0; j < col; ++j) {
mat[i][j] = ADD(mat[i][j], b[i][j]);
}
}
return *this;
}
friend Semiring_Matrix operator+(const Semiring_Matrix& a, const Semiring_Matrix& b) { return Semiring_Matrix(a) += b; }
friend Semiring_Matrix operator*(const Semiring_Matrix& a, const Semiring_Matrix& b) {
assert(a.col == b.row);
Semiring_Matrix res(a.row, b.col);
for (int i = 0; i < a.row; ++i) {
for (int k = 0; k < a.col; ++k) {
for (int j = 0; j < b.col; ++j) {
res[i][j] = ADD(res[i][j], MUL(a[i][k], b[k][j]));
}
}
}
return res;
}
Semiring_Matrix& operator*=(const Semiring_Matrix& b) { return *this = *this * b; }
Semiring_Matrix transpose() const {
Semiring_Matrix res(col, row);
for (int i = 0; i < row; ++i) {
for (int j = 0; j < col; ++j) {
res[j][i] = mat[i][j];
}
}
return res;
}
friend ostream& operator<<(ostream& os, const Semiring_Matrix& m) {
for (int i = 0; i < m.row; ++i) {
for (int j = 0; j < m.col; ++j) {
os << m[i][j] << (j == m.col - 1 ? "" : " ");
}
if (i != m.row - 1) os << "\n";
}
return os;
}
private:
vector<vector<Semiring>> mat;
};
template<class Semiring, auto ADD, auto zero, auto MUL, auto one>
Semiring_Matrix<Semiring, ADD, zero, MUL, one> power(Semiring_Matrix<Semiring, ADD, zero, MUL, one> A, int64_t n) {
assert(A.row == A.col);
assert(n >= 0);
auto res = Semiring_Matrix<Semiring, ADD, zero, MUL, one>::identity(A.row);
while (n > 0) {
if (n & 1) res *= A;
A *= A;
n >>= 1;
}
return res;
}
#line 6 "1780.test.cpp"
using ell = Extended_Algebra<ll>;
ell op_max(ell a, ell b) { return max(a, b); }
using Mat = Semiring_Matrix<ell, op_max, -ell::inf, add<ell>, ell(0)>;
int color = 16, member = 26;
ell solve() {
vector<int> C(member); cin >> C;
vector<int> K(member); cin >> K;
vector<Mat> mat(member, Mat::identity(color));
int N; cin >> N;
for (int i = 1; i <= N; ++i) {
string S; int A, B; ll E;
cin >> S >> A >> B >> E;
--A; --B;
for (auto z: S) {
chmax(mat[z - 'A'][A][B], ell(E));
chmax(mat[z - 'A'][B][A], ell(E));
}
}
vector<ell> V(color);
for (int z = 0; z < member; ++z) {
Mat tmp = power(mat[z], K[z]);
for (int c = 0; c < color; ++c) {
V[c] += tmp[C[z] - 1][c];
}
}
return max(V);
}
int main() {
ell ans = solve();
if (ans.is_negative_infinite()) cout << "Impossible" << endl;
else cout << ans << endl;
}